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Beyond Volume Overlap: Surface Matching for Topology-Aware Coronary Artery Segmentation
Rafael Velasquez, Esther Puyol-Antón, Pablo Arbeláez
TL;DR
Dice-based overlap metrics can obscure errors in thin coronary vessels, where connectivity matters for downstream clinical workflows. The paper introduces an adaptive surface metric and differentiable surface loss; against a matched-epoch control, the loss improves surface F1 while reducing missed vessels. The authors caution that distal-branch annotation quality limits what these gains establish.
Problem
Dice-based training and evaluation are poorly suited to thin, tubular vessels, where broken branches can have little effect on volume overlap despite disrupting clinically relevant connectivity.
Source: §1 · p. 2Method
The paper matches predicted and reference surface points by bipartite assignment under local vessel-radius tolerance and proposes a differentiable surface loss targeting missed and spurious structure.
Source: §1 · p. 2, §2 · p. 3, §2.1 · p. 3Results
Surface F1 rises from 79.50 to 82.60 against a matched-epoch control, while false negatives drop 22,124→15,798 (−29%) and false positives also fall 14,972→13,215.
Source: §4.2 · p. 8Takeaways & Limitations
The surface metric reveals that the Dice+CE baseline omits more vessel surface than it hallucinates, and surface loss improves surface F1 by recovering missed distal vessels.
Source: §4.1 · p. 7, §4.2 · p. 8Distal-recall gains on public benchmarks indicate improved agreement with available annotations, not proof of anatomically correct recovery, because distal-branch annotations have reported inconsistencies and biases.
Source: §4.4 · p. 10
Abstract
from arXiv · showhide
Accurate coronary artery segmentation on coronary computed tomography angiography (CCTA) is essential for diagnosing coronary artery disease. Deep networks are conventionally trained and evaluated with the Dice coefficient, but volume-overlap metrics are poorly suited to thin, tubular anatomy: since most voxels belong to a few thickproximal segments, a missing distal branch barely affects Dice despite severely disrupting the connectivity required for clinical use. We introduce a surface metric that matches predicted and reference surface points via bipartite assignment under a localized, vessel-radius tolerance, reporting precision, recall, and F1 with decoupled false positives (spurious branches) and false negatives (missed branches) a distinction the symmetric Dice cannot make. With it we show that a strong Dice-trained baseline omits far more vessel surface than it hallucinates, an asymmetry its high Dice hides. Building on this, we propose a differentiable surface loss that simultaneously suppresses spurious mass and recovers absent structure, validated by fine-tuning three backbones (nnU-Net, SwinUNETR, NexToU) on two public benchmarks (Image-CAS, ASOCA). Against a matched-epoch control, it significantly improves surface F1 by recovering missed distal vessels at comparable Dice. Our findings argue for measuring and optimizing the vessel surface, not the volume it overlaps. Code
1 Introduction
Coronary segmentation supports downstream diagnosis, but Dice-based training and evaluation are poorly suited to thin, tubular vessels and can conceal clinically important connectivity errors. The paper introduces an adaptive surface-matching metric and a differentiable surface loss, then evaluates them on public benchmarks.
1 Introduction
- Connected vessel trees matter for downstream CCTA workflows, including FFR-CT modeling and centerline-based stenosis detection.Fragmented vessel masks cause centerline-based detection pipelines to fail.Source: §1 · p. 2
- Dice is poorly suited to thin vessels: thick proximal segments dominate its score, while broken branches and hallucinated bridges can alter only a few voxels.It also conflates missed vessels with spurious branches in one symmetric score.Source: §1 · p. 2
- Topology-aware alternatives include clDice and Betti-error losses, but the proposed metric evaluates full vessel surfaces with local-radius tolerance and absolute, decoupled error counts.Unlike clDice’s skeleton-based components, it localizes errors at the scale of vessel calibre.Source: §1 · p. 2
- Bipartite surface matching uses vessel-radius-adaptive tolerance so missed branches reduce recall and hallucinated branches reduce precision.Thin distal branches therefore require sub-millimeter agreement.Source: §1 · p. 2
- The paper also proposes a differentiable surface loss whose gradients recover missed distal geometry while suppressing spurious artifacts, and validates it on two public benchmarks across three backbones.The experiments isolate the optimization objective from network architecture; the code is publicly available.Source: §1 · p. 3
2 Method
The method evaluates coronary segmentation by matching full predicted and reference surfaces with a vessel-radius tolerance, then trains with surface-based terms for spurious and missed structure. The radius is derived from the reference anatomy, and the surface objective is added to the backbone loss with warm-up and magnitude rescaling.
2 Method
- Reference surface radii come from the Euclidean distance transform’s medial ridge and are assigned from the nearest ridge voxel, without centreline annotations.The distance transform and ridge use physical voxel spacing, making the radius represent 3D vessel calibre independent of slice orientation.Source: §2 · p. 3
2.1 Bipartite Surface Metric
- A one-to-one assignment matches full predicted and reference surface point sets within each reference point’s local vessel-radius tolerance, leaving unmatched points as distinct false positives or false negatives.The method retains the full point counts rather than subsampling to equal sizes; matches are greedily assigned in increasing distance order.Source: §2.1 · pp. 3–4, Figure 1 · p. 4
2.2 Surface Loss
- The surface loss combines removal and creation terms: one penalizes probability far outside the vessel, while the other weights low probability on the reference surface by distance from predicted mass.An entirely missed branch lies far from predicted mass, so the creation term pushes probability up along the missed branch; surface weighting treats thin distal and thick proximal segments equally.Source: §2.2 · p. 4, Removal term (false positives) · p. 5, Creation term (false negatives) · p. 5
- The combined surface loss is added to the standard deep-supervised backbone loss with linear warm-up and rescaling by a detached running estimate of its magnitude relative to the base loss.The target fraction of the base loss is set by λmax, avoiding manual tuning; the surface term is applied to the highest-resolution deep-supervision head.Source: Total objective · p. 5
- Compared with boundary loss, the creation term uses distance to current predicted mass, giving entirely missed branches a growing gradient; the authors report over 5,000 fewer missed surface points than cbDice.The loss acts on surface points rather than integrating an interior distance field that scales with vessel calibre.Source: Total objective · p. 6
3 Experiments
Experiments use two public CCTA benchmarks and three 3D backbones under a shared fine-tuning protocol. They compare topology- and distance-aware losses with Dice+CE using volume, topology, and surface metrics.
Datasets
- ImageCAS uses 800 training volumes with five-fold cross-validation and 200 held-out tests; ASOCA uses 32 training cases with five-fold cross-validation and eight held-out tests.ASOCA’s folds and test split preserve the balance of 20 normal and 20 diseased cases.Source: Datasets · p. 6
Backbones, training, and baselines
- nnU-Net, SwinUNETR, and NexToU are compared after 150-epoch fine-tuning from 1000-epoch Dice+CE baselines, with a matched-epoch continued-training control.The common comparison includes clDice, cbDice, and the proposed surface loss.Source: Backbones, training, and baselines · p. 6
Evaluation
- Evaluation reports Dice, clDice, Betti-number absolute error, and surface precision, recall, and F1, with paired Wilcoxon tests and Holm correction for comparisons against Dice+CE.Source: Evaluation · p. 7
4 Results and Discussion
The Dice+CE baseline’s high overlap score masks disproportionate misses in thin distal vessels. Surface-loss fine-tuning improves surface F1 across backbones at comparable Dice, while metric checks show error-specific responses and stable method rankings across tolerance choices.
4.1 What Dice Cannot See
- At mean Dice 80.99, the baseline had 22,124 missed versus 14,972 spurious surface points; thin branches were missed at 39.5%, versus 4.5% for thick segments.Thin branches account for 1.2% of vessel volume, while thick proximal segments account for 74.9%; baseline topology differed by 6.14 ± 3.6 connected components.Source: §4.1 · p. 7, Table 1 · p. 7
4.2 Main Comparison
- Surface F1 rose from 79.50 to 82.60 on nnU-Net, with significant gains across all three backbones; Dice rose modestly from 80.99 to 82.05, and ASOCA showed the same direction.The matched-epoch control isolates the gain from longer training; ASOCA has only eight test cases, so its results are corroborative.Source: §4.2 · pp. 7–9, Table 2 · p. 8, Table 3 · p. 8
4.3 Metric Validation and Sensitivity Analysis
- Removing thin branches lowered recall monotonically while precision stayed high, whereas adding spurious mass lowered precision while recall stayed high.The controlled perturbations show that the metric assigns each error mode to its corresponding precision or recall component.Source: §4.3 · pp. 9–10
- Method rankings persisted when the reference-derived radius tolerance was rescaled from 0.5 to 2.0, although absolute F1 values shifted.Surface F1 also remained stable under subsampling to 50% density, with standard deviation below the reported F1-point threshold.Source: §4.3 · p. 10
4.4 Limitations and Dataset Considerations
- Known annotation inconsistencies in public datasets, especially for secondary and tertiary ASOCA branches, limit interpreting distal-recall gains as anatomically correct recovery.The authors motivate future evaluation using datasets with independently adjudicated distal annotations.Source: §4.4 · p. 10
5 Conclusion
The surface loss improves surface F1 and connectivity across three architectures on ImageCAS and ASOCA, while prioritizing boundary geometry over volume overlap. Extending the method to native 3D point clouds remains future work because local vessel radius must be estimated directly from the points.
5 Conclusion
- Consistent gains in surface F1 and connectivity across three architectures on ImageCAS and ASOCA support the surface loss’s effectiveness.Its creation and removal terms target missed branches and spurious mass, respectively.Source: §5 · pp. 10–11
- The authors conclude that boundary geometry should be prioritized over volume overlap for coronary segmentation.They note that this approach extends naturally to multi-scale hepatic and cerebrovascular networks.Source: §5 · p. 11
- The current voxel-mask implementation uses Marching Cubes; applying the method to native 3D point clouds would require estimating local radius from the points, which is left for future work.Source: §5 · p. 11